I’ve been watching the TV series Pantheon and I really like it, but this tiny aspect is something I can’t quite grasp. So these people have their minds uploaded to the cloud - and they make a point to state that they’re still “them” - alive, real, authentic. But would it really be like that? The process is brain mapping, so essentially they just make a perfect clone of your brain/mind and run it digitally. But it’s still just a simulation. A perfect clone is still just a clone. The original person is gone. I don’t see the “continuity” aspect.
A copy wouldn’t be you. But sometimes sci-fi uses transferrence, where your consciousness isn’t just duplicated, it’s actually moved over to the new body/machine. See stuff like Ghost in the Shell.
I don’t think transferrance is all that realistic though. Making a digital copy is a more realistic thing.
Maybe if you handle it like the ship of Theseus? Replace a few cells and little brain function over a long time (so that the body can adapt) by some compatible future machine.
Maybe in the end you are a full cyborg, not just a cyborg copy.